Purity of Methods

Andrew Arana
University of Paris 1 Panthéon-Sorbonne
Throughout history, mathematicians have expressed preference for solutions to problems that avoid introducing concepts that are in one sense or another “foreign” or “alien” to the problem under investigation. This preference for “purity” (which German writers commonly referred to as “methoden Reinheit”) has taken various forms. It has also been persistent. This notwithstanding, it has not been analyzed at even a basic philosophical level. In this paper we give a basic analysis of one conception of purity—what we call topical purity—and discuss its epistemological significance
Keywords proof  purity
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On the Relationship Between Plane and Solid Geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
Formalization, Primitive Concepts, and Purity.John T. Baldwin - 2013 - Review of Symbolic Logic 6 (1):1-42.
Rota's Philosophy in its Mathematical Context.Sébastien Gandon - 2016 - Philosophia Mathematica 24 (2):145-184.

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